Recursive Matrix Decomposition Methods and Applications in Wireless Communication

Matrix decomposition methods such as the Cholesky and the QR decomposition arise in several applications in signal processing for multiple-input, multiple-output (MIMO) communication systems. The computational complexity of regular Cholesky and QR solvers is known to be $\mathcal{O}\left( {{N^3}} \right)$. To reduce this, several recursive algorithms at both column- and block-levels have been proposed in the literature. In this paper, we utilize one such recursive structure in Cholesky and QR decompositions for matrices with entries from the field of complex numbers, which results in a level of complexity reduction. The use of the considered techniques is discussed in the context of a MIMO decoder. In particular, the utility of proposed methods is illustrated in a MIMO successive interference cancellation based detector. Simulation results are provided to substantiate the performance of a detector under two different antenna and receiver configurations.